In order to easily determine the hydrocarbon reserves (gas, petrol or oils) of reservoirs in operation or reservoirs to be operated, geologists most often manipulate and study two-dimensional maps that represent the “HuPhiSo” (referred to as “HuPhiSo” maps). Indeed, these maps are summarised and quickly provide the geologist with information as to the economic value of the reservoir (3D).
For a three-dimensional rock volume, the “HuPhiSo” map (in two dimensions) comprises a plurality of values, with each value being the product of several parameters:HuPhiSo=h·NTG·φ·So 
with the parameter h being the height of the column (according to the axis {right arrow over (z)} if the map is according to the plane ({right arrow over (x)},{right arrow over (y)})), the parameter NTG (“Net to Gross”) being the fraction of the rock volume favourable to the presence of hydrocarbons, with the parameter φ being the porosity of the rock and the parameter So being the oil saturation of the porosities.
As such, if V is the rock volume considered, V·NTG·Phi So is the volume of oil contained in the rock volume. A value “HuPhiSo” represents the “height of the column of oil” in a column under consideration. However, this value is indirectly connected to the volume of the oil and can represent the “surface density of the oil”.
For a model meshed with parallelepiped cells, it is possible to calculate a “HuPhiSo” value for the final map by summing the value “HuPhiSo” of each cell of a column of this model.
Of course, the determining of the “HuPhiSo” values can be simple if the parameters h, NTG, Phi and So are known for certain for any point/cell of the model. However, in practice, these parameters are perfectly known only in a few isolated points: the points of the drilling wells. Of course, it is possible to simulate these parameters for the other cells thanks to the crossing of various data analyses (ex. seismic) and the use of stochastic simulation algorithms based on geostatistical methods in order to “supplement” the model. To this is added the natural distribution of the petrol-physical properties (acoustic impedance, effective porosity, porosity of the rocks in the NTG, etc.). Each physical magnitude can therefore be considered as a random variable, possibly non-stationary (ex. the porosity decreases most often with the depth).
There are a large number of uncertainties that weigh on the various parameters on which the HuPhiSo map depends, in such a way that the latter can vary substantially from one possible map to another.
For making decisions, reservoir engineers particularly appreciate the maps of expectation of the HuPhiSo and maps of expectation (or of variance) around the expectation of the HuPhiSo.
Usually, these maps are obtained by simulating a large number of HuPhiSo maps. For each cell of the map, an average and a variance are then calculated according to the corresponding cells in the simulated HuPhiSo maps.
However, each simulation can be costly in terms of resources and in calculation time and it is not rare for the determining of maps of expectation and standard deviation to take several hundred hours.
There is therefore a need for determining an average HuPhiSo map (expectation) and/or of the interval of uncertainties corresponding to this map (variance or standard deviation) more quickly, without carrying out a large number of simulations of HuPhiSo maps.